1Function: algpoleval
2Section: algebras
3C-Name: algpoleval
4Prototype: GGG
5Help: algpoleval(al,T,b): T in K[X] evaluate T(b) in al.
6Doc: Given an element $b$ in \var{al} and a polynomial $T$ in $K[X]$,
7 computes~$T(b)$ in~\var{al}. Also accepts as input a \typ{VEC}~$[b,mb]$
8 where~$mb$ is the left multiplication table of~$b$.
9
10 \bprog
11 ? nf = nfinit(y^2-5);
12 ? al = alginit(nf,[y,-1]);
13 ? b = [1..8]~;
14 ? pol = algcharpoly(al,b,,1);
15 ? algpoleval(al,pol,b)==0
16 %5 = 1
17 ? mb = algtomatrix(al,b,1);
18 ? algpoleval(al,pol,[b,mb])==0
19 %7 = 1
20 @eprog
21